非概率响应面界限法在桥梁可靠性评估中的应用
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摘要
桥梁结构中各种不确定性的存在加大了可靠性评估的难度,而且对于复杂桥梁往往难以获取相应的功能函数。本文针对上述问题提出基于非概率可靠性理论的响应面界限法,用于求解非概率可靠性指标,评估在役桥梁的可靠性,建立一套适用于在役桥梁的非概率可靠性评估流程。研究以三跨PC连续刚构桥为例,通过确定区间变量参数,利用Midas软件建立桥梁有限元模型;以中跨的跨中截面为控制截面,获取极限弯矩等参数,利用Matlab软件对获取的数据进行处理,并利用提出的响应面界限法求解非概率可靠性指标η,结果为η=1.15762>1,表明在役桥梁处于可靠状态。算例分析表明,基于响应面界限法的非概率可靠性评估方法,便于求解非概率可靠度指标,对在役桥梁进行可靠性评估具有较强的优势。
Uncertainties in bridge structures gave rise to difficultly conducting the non-probabilistic reliability evaluation of existing bridges and difficultly obtaining the performance function for complicated bridge structures. This paper presented the non-probabilistic response surface limit method based on non-probabilistic reliability theory to solve these problems. The presented response surface limit method was used to evaluate the non-probabilistic reliability of existing bridges by solving non-probabilistic reliability index. Then the non-probabilistic reliability evaluation process for existing bridges was built. Taking a three-span PC continuous rigid frame bridge as an example, by determining the interval variables,the finite element model was built utilizing the Midas software. The middle section of the middle span was selected as the control section,the ultimate bending moment and other parameters were obtained,and the data obtained was processed using the Matlab software.The non-probabilistic reliability index was solved and that was η = 1.15762>1,therefore,the existing bridge was reliable. The illustrative example showed that,using the presented non-probabilistic reliability evaluation methods was convenient to solve non-probabilistic reliability index,and there was a great advantage in estimating the non-probabilistic reliability of existing bridges.
Uncertainties in bridge structures gave rise to difficultly conducting the non-probabilistic reliability evaluation of existing bridges and difficultly obtaining the performance function for complicated bridge structures. This paper presented the non-probabilistic response surface limit method based on non-probabilistic reliability theory to solve these problems. The presented response surface limit method was used to evaluate the non-probabilistic reliability of existing bridges by solving non-probabilistic reliability index. Then the non-probabilistic reliability evaluation process for existing bridges was built. Taking a three-span PC continuous rigid frame bridge as an example, by determining the interval variables,the finite element model was built utilizing the Midas software. The middle section of the middle span was selected as the control section,the ultimate bending moment and other parameters were obtained,and the data obtained was processed using the Matlab software.The non-probabilistic reliability index was solved and that was η = 1.15762>1,therefore,the existing bridge was reliable. The illustrative example showed that,using the presented non-probabilistic reliability evaluation methods was convenient to solve non-probabilistic reliability index,and there was a great advantage in estimating the non-probabilistic reliability of existing bridges.
引文
[1]焦美菊,孙利民,李清富.基于检测数据的桥梁结构可靠性评估[J].同济大学学报(自然科学版),2011,39(10):1452-1457.
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[4]Qiao X Z.A non-probabilistic measure of structural reliability based on convex model[J].Advanced Materials Research,2014,912-914:1103-1107.
[5]Meng Z,Zhou H L,Li G,et al.A decoupled approach for non-probabilistic reliability-based design optimization[J].Computers and Structures,2016,175:65-73.
[6]Li Y L,Wang X J,Wang L,et al.Non-probabilistic stability reliability measure for active vibration control system with interval parameters[J].Journal of Sound and Vibration,2017,387:1-15.
[7]陈旭勇,樊建平.非概率可靠性中一维优化算法的改进及其在桥梁评估中应用[J].工程力学,2011,28(5):21-25.
[8]Peng W J,Huang X X,Ge R.The analysis and optimization of the reliability of laminates based on probabilistic and non-probabilistic hybrid model[J].Advanced Materials Research,2013,629:752-756.
[9]陈旭勇,胡海棠,高兵勇.非概率可靠性在拱桥评估与加固中的应用[J].桥梁建设,2016,46(2):60-64.
[10]Li S J,Chen X Y.Non-probabilistic reliability of RC bridge retrofitted in flexure with externally bonded steel plates[J].Applied Mechanics and Materials,2013,351-352:1590-1595.
[11]Wang L,Wang X J,Su H,et al.Reliability estimation of fatigue crack growth prediction via limited measured data[J].International Journal of Mechanical Sciences,2017,121:44-57.
[12]Wang L,Wang X J,Wang R X,et al.Reliabilitybased design optimization under mixture of random,interval and convex uncertainties[J].Archive of Applied Mechanics,2016,86(7):1341-1367.
[13]江涛,陈建军,姜培刚,等.区间模型非概率可靠性指标的一维优化算法[J].工程力学,2007,24(7):23-27.
[14]李世军,樊建平,漆炜,等.非概率区间模型可靠性指标的梯度投影算法[J].计算力学学报,2013,30(2):192-197.
[15]Chen X Y,Fan J P,Bian X Y.Theoretical analysis of non-probabilistic reliability based on interval model[J].Acta Mechanica Solida Sinica,2017,30(6):638-646.
[16]樊建平,李世军,陈旭勇.非概率可靠性指标空间搜索算法[J].计算力学学报,2012,29(6):831-834.
[17]Box G E P,Wilson K B.On the experimental attainment of optimum conditions[J].Journal of the Royal Statistical Society,1951,13(1):1-45.
[18]许长城.体外预应力技术在连续刚构桥中的应用研究[D].重庆:重庆交通大学,2008.
[19]吴光宇,林伟,汪劲丰,等.有效预应力对大跨P.C.桥梁极限承载力的影响研究[J].计算力学学报,2013,30(3):362-369.
[20]GB 50010-2010,混凝土结构设计规范(2015版)[S].
[21]GB/T 5224-2014,预应力混凝土用钢绞线[S].
[2]李亚东.既有桥梁评估方法研究[J].铁道学报,1997,19(3):109-115.
[3]陈旭勇,樊建平.凸集模型非概率可靠性在桥梁评估中的应用[J].华中科技大学学报(自然科学版),2009,37(12):120-123.
[4]Qiao X Z.A non-probabilistic measure of structural reliability based on convex model[J].Advanced Materials Research,2014,912-914:1103-1107.
[5]Meng Z,Zhou H L,Li G,et al.A decoupled approach for non-probabilistic reliability-based design optimization[J].Computers and Structures,2016,175:65-73.
[6]Li Y L,Wang X J,Wang L,et al.Non-probabilistic stability reliability measure for active vibration control system with interval parameters[J].Journal of Sound and Vibration,2017,387:1-15.
[7]陈旭勇,樊建平.非概率可靠性中一维优化算法的改进及其在桥梁评估中应用[J].工程力学,2011,28(5):21-25.
[8]Peng W J,Huang X X,Ge R.The analysis and optimization of the reliability of laminates based on probabilistic and non-probabilistic hybrid model[J].Advanced Materials Research,2013,629:752-756.
[9]陈旭勇,胡海棠,高兵勇.非概率可靠性在拱桥评估与加固中的应用[J].桥梁建设,2016,46(2):60-64.
[10]Li S J,Chen X Y.Non-probabilistic reliability of RC bridge retrofitted in flexure with externally bonded steel plates[J].Applied Mechanics and Materials,2013,351-352:1590-1595.
[11]Wang L,Wang X J,Su H,et al.Reliability estimation of fatigue crack growth prediction via limited measured data[J].International Journal of Mechanical Sciences,2017,121:44-57.
[12]Wang L,Wang X J,Wang R X,et al.Reliabilitybased design optimization under mixture of random,interval and convex uncertainties[J].Archive of Applied Mechanics,2016,86(7):1341-1367.
[13]江涛,陈建军,姜培刚,等.区间模型非概率可靠性指标的一维优化算法[J].工程力学,2007,24(7):23-27.
[14]李世军,樊建平,漆炜,等.非概率区间模型可靠性指标的梯度投影算法[J].计算力学学报,2013,30(2):192-197.
[15]Chen X Y,Fan J P,Bian X Y.Theoretical analysis of non-probabilistic reliability based on interval model[J].Acta Mechanica Solida Sinica,2017,30(6):638-646.
[16]樊建平,李世军,陈旭勇.非概率可靠性指标空间搜索算法[J].计算力学学报,2012,29(6):831-834.
[17]Box G E P,Wilson K B.On the experimental attainment of optimum conditions[J].Journal of the Royal Statistical Society,1951,13(1):1-45.
[18]许长城.体外预应力技术在连续刚构桥中的应用研究[D].重庆:重庆交通大学,2008.
[19]吴光宇,林伟,汪劲丰,等.有效预应力对大跨P.C.桥梁极限承载力的影响研究[J].计算力学学报,2013,30(3):362-369.
[20]GB 50010-2010,混凝土结构设计规范(2015版)[S].
[21]GB/T 5224-2014,预应力混凝土用钢绞线[S].